Field-of-view compensated polarization switch for short-throw 3D projection

ABSTRACT

Generally, this disclosure concerns the angle sensitivity of polarization switch elements and the resulting impact of the ray direction on performance. More specifically, apparatus and techniques for compensating the angular sensitivity of liquid crystal (LC) polarization switches are described that enhance the performance of polarization switches. For example, a polarization switch is disclosed that transforms linearly polarized light of an initial polarization orientation that includes a first and second liquid crystal cell with a compensator located between the LC cells. The compensator layer is operable to enhance the field of view through the polarization switch. Such compensation techniques are particularly useful for short-throw projection environments.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority to (1) U.S. Provisional PatentApplication Ser. No. 61/363,826, filed Jul. 13, 2010, entitled“Field-Of-View Compensated Polarization Switch for Short-Throw 3DProjection,” and also claims priority to (2) U.S. Provisional PatentApplication Ser. No. 61/384,629, filed Sep. 20, 2010, entitled“Field-Of-View Compensated Polarization Switch for Short-Throw 3DProjection,” the entirety of both is herein incorporated by reference.

TECHNICAL FIELD

This disclosure generally relates to stereoscopic display systems. Inparticular, it relates to sequential 3D stereoscopic displays, includingshort-throw projection systems and direct view displays withpolarization switches that exhibit high contrast at a large angle ofincidence.

BACKGROUND

Modern stereoscopic 3D cinema typically utilizes a single digitalprojector synchronized with a polarization switch as a means ofdelivering two views. Passive polarizing eyewear decodes the sequentialimages, delivering the appropriate perspective to each eye. At thesystem level, one eye receives the appropriate perspective image whilethe other (ideally) receives little to substantially no information. Inthe likely event that a percentage of the improper image leaks when theshutter is in the closed-state, the quality of the 3D experience isdegraded. The level of this ghost image depends upon many contributors,which can include the projector, the polarization switch, the screen,the eyewear, and the geometry associated with a ray through the system.

BRIEF SUMMARY

In direct view sequential 3D, a polarization switch can be placed at theoutput of the display. This can include an LCD, a plasma display, anOLED, or any suitable display technology. The polarization switch isoperated synchronously with the display, and may include a scrollingshutter, as described in pending applications, e.g., U.S. patentapplication Ser. Nos. 12/156,683; 12/853,274; 12/853,279; and12/853,265, all of which are herein incorporated by reference. In orderthat multiple viewers have a similar high contrast experience, it isdesirable that the shuttering operation is effective when the display isviewed from many different angles. This may require an acceptable 3Dexperience at half-angles exceeding 40-degrees horizontal. Conventionalpolarization switches, such as the ZScreen, do not offer suchperformance.

The angle sensitivity of polarization switch elements and the resultingimpact of the ray direction on performance and methods for enhancingperformance by compensating for such effects are discussed herein. Morespecifically, methods for compensating the angular sensitivity of liquidcrystal (LC) polarization switches are described. In one embodiment, thesymmetry of a dual-cell polarization switch may be utilized to introduceone or more compensation layers that may enhance the contrast andefficiency over a range of angles.

In another embodiment, compensation layers may be introduced. A firstcompensation layer may be located between the LC cells, and a secondcompensation layer may be located between the analyzing circularpolarizer and the polarization switch, to further enhance the FOV. Inone embodiment, both compensators are negative C-plates, in which theretardation of the compensator between the cells has approximately thesame (splay-state) retardation as the LC cell, while the compensatorbetween the viewer and the ZScreen has approximately half of the(splay-state) retardation of the cell.

These and other advantages and features of the present disclosure willbecome apparent to those of ordinary skill in the art upon reading thisdisclosure in its entirety.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments are illustrated by way of example in the accompanyingfigures, in which like reference numbers indicate similar parts, and inwhich:

FIG. 1 is a schematic diagram illustrating the operation of an exemplarythree-dimensional movie projection system, in accordance with thepresent disclosure;

FIG. 2A illustrates the layout of a ZScreen with analyzing eyewear, inaccordance with the present disclosure;

FIG. 2B illustrates another layout of a ZScreen with analyzing eyewear,in accordance with the present disclosure;

FIG. 3 is a graph illustrating the ON-state spectrum fornormal-incidence and two substandard-case azimuth angles, in accordancewith the present disclosure;

FIG. 4 is a polar plot of the OFF-state leakage of an uncompensatedZScreen, out to a maximum incidence angle of 30°, in accordance with thepresent disclosure;

FIG. 5 is a polar plot of the OFF-state leakage of an uncompensatedZScreen, out to a maximum incidence angle of 30°, in accordance with thepresent disclosure;

FIG. 6A is a polar plot showing an OFF-state polar leakage plot with−550 nm of negative C-plate retardation, corresponding to the stateshown in FIG. 2A, in accordance with the present disclosure;

FIG. 6B is a polar plot showing an OFF-state polar leakage plot with−500 nm and −250 nm of negative C-plate retardation, corresponding tothe state shown in FIG. 2B, in accordance with the present disclosure;

FIG. 7A is a polar plot showing an OFF-state polar leakage plot with−550 nm of negative C-plate retardation, corresponding to the stateshown in FIG. 4, in accordance with the present disclosure; and

FIG. 7B is a polar plot showing an OFF-state polar leakage plot with−500 nm and −250 nm of negative C-plate retardation, corresponding tothe state shown in FIG. 4, in accordance with the present disclosure.

DETAILED DESCRIPTION

Generally, the present disclosure concerns the angle sensitivity of thepolarization switch elements and the resulting impact of the raydirection on performance. Techniques for enhancing the performance bycompensating for such effects are disclosed. More specifically,apparatus and methods for compensating the angular sensitivity of liquidcrystal (LC) polarization switches are described herein. In oneembodiment, the symmetry of a dual-cell polarization switch may beutilized to introduce one or more compensation layers that enhance thecontrast and efficiency over a range of angles. Furthermore, acompensation layer may be located between the polarization switch andthe analyzing circular polarizer eyewear to further enhance at least thecontrast and efficiency over a range of angles. The latter may beaffixed to the polarization switch between the exit LC cell and a glassend-cap.

It should be noted that embodiments of the present disclosure may beused in a variety of optical systems and projection systems. Theembodiments may include or work with a variety of projectors, projectionsystems, optical components, computer systems, processors,self-contained projector systems, visual and/or audiovisual systems andelectrical and/or optical devices. Aspects of the present disclosure maybe used with practically any apparatus related to optical and electricaldevices, optical systems, presentation systems or any apparatus that maycontain any type of optical system using a polarization switch.Accordingly, embodiments of the present disclosure may be employed inoptical systems, devices used in visual and/or optical presentations,visual peripherals and so on and in a number of computing and/ortelecommunications environments.

Before proceeding to the disclosed embodiments in detail, it should beunderstood that the disclosure is not limited in its application orcreation to the details of the particular arrangements shown, becausethe disclosure is capable of other embodiments. Moreover, aspects of thedisclosure may be set forth in different combinations and arrangementsto define embodiments unique in their own right. Also, the terminologyused herein is for the purpose of description and not of limitation.

FIG. 1 is a schematic diagram illustrating the operation of astereoscopic three-dimensional movie projection system 100 using asingle-projector (sequential) platform 120. In operation, left-eyeimages 102 and right-eye images 104 may be projected sequentially fromthe projector 120 through polarization switch 122 toward apolarization-preserving screen 110. Polarization-preserving screen 110allows the polarized light from the projector 120 and polarizationswitch 122 to be reflected to the moviegoer 140. The left- and right-eyeimages are viewed by the moviegoer 140 wearing eyewear 150 that decodesthe respective orthogonally polarized light to create the experience ofdepth for object 106. Generally, the quality of the stereoscopic viewingexperience may depend upon the ability of the system 100 to preserve thehigh degree of polarization transmitted by the projector platform 120.

Currently, LC polarization switches 122 may be operated at the output ofthe projection lens. Throw ratios can vary considerably depending upontheatre geometry. Throw ratio is defined as the ratio of distance fromthe projector-to-screen to the screen width. Stated differently, thethrow ratio may be expressed:

Throw ratio=D/W

The distance D and width W are shown in FIG. 1.

Low throw-ratios, for example less than 1.2, in which the projector isapproximately 1.2 feet away from the screen for every foot of screenwidth, may place significant demands on the angular performance of LCelements, which may lead to contrast and efficiency loss. It is notuncommon for the ray to exceed approximately 25° with respect to normal,in air, as shown by FIG. 1.

A ZScreen is an example of a polarization switch 122 which may have aninput linear polarizing means, followed by a pair of LC elements(π-cells) with crossed rubbing directions, oriented at approximately±45° with respect to the polarizer. Examples may include, U.S. Pat. No.4,792,850, FIGS. 3-11 and the related description. Examples of ZScreenpolarization switches are described in commonly-assigned U.S. Pat. No.4,792,850, and 7,633,666 to Lipton et al., both of which are hereinincorporated by reference. Another example of a polarization switch isdescribed with reference to commonly-owned U.S. Pat. No. 7,528,906 toRobinson, herein incorporated by reference.

With reference to the ZScreen, the π-cells operate substantiallysynchronously, such that when one cell is in a high voltage state (VH),the other cell may be in a low voltage state (VL), or holding voltage.When the voltages are swapped, the cells may collectively behave like aquarter-wave retarder with optic axis switchable between orientations ofapproximately ±45°. When paired with matched circular polarizing eyewearlenses, the result in principle, may be a high contrast neutraloff-state, with the chromatic on-state associated with a zero-orderhalf-wave retarder. This relatively ideal set of circumstances breaksdown when the ray direction through the ZScreen deviates from the normaldirection.

At approximately normal incidence, the π-cell functions as a linearvariable retarder. However, the π-cell may not function as a linearvariable retarder at other incidence angles, due to the inhomogeneity ofthe director profile. One consequence of the director distributionassociated with a π-cell is that the cell contains significantly greaterretardation than is required to accomplish the required switching. Forinstance, it may be desirable to use a cell with over approximately 500nm of retardation in order to deliver approximately 140 nm of switching.This additional retardation may have a negative impact on Field of View(FOV) performance. In general, the behavior is not a pure retardationshift off-normal, due to the director profile. As such, techniques forincreasing the FOV using film compensation have limited effectiveness.

Polarization compensators are generally described in the book by G.Sharp et al., Polarization Engineering for LCD Projection (2005), hereinincorporated by reference. Polarization compensators may be used toenhance the FOV of direct view LC displays. The compensation scheme maydepend upon the LC mode and cell recipe. Several modes may be used incurrent LCD products, including In Plane Switching (IPS), VerticallyAligned (VA), and Twisted Nematic (TN) products, with a compensationscheme for each. There are many compensator films available, with arelatively large number of options for A-plate and C-plate behavior,with compensators having O-plate (oblique) behavior being relativelyrare. Examples of the former or both the A-plate and the C-plate, aremanufactured by casting/extrusion and stretching of polymer films. Anexample of the latter or O-plate is the WV film supplied by Fuji, havinga discotic LC polymer coated on a Triacetylcellulose (TAC) sheet. It isadvantageous to identify compensation schemes which are effective, butare also plentiful in supply, with multiple suppliers.

Polarization switches, unlike active matrix display devices, may beoperated at relatively high voltage levels. One benefit of operating atthese voltage levels may include more rapid switching, while maximizingretardation swing. This has the further benefit of substantiallyhomogenizing the director profile in the fully energized state, thusincreasing the effectiveness of the compensation. A π-cell in the VHstate may behave substantially like a positive C-plate, provided thatthe voltage is sufficiently high. That is, the LC material behaves likea positive uniaxial retarder with optic axis approximately normal to thesubstrate. According to the present disclosure, the VH voltage amplitudemay exceed approximately 20V, for example, across an approximately 3.5micron cell, in order to achieve a substantially homogeneous directorprofile. A DC balanced waveform may be used to insure long-termreliability and performance of the cell, which may otherwise be degradedby ion migration. While unswitched material may remain at the boundary,it may have little impact on performance provided that the voltage isadequate. Conversely, the π-cell in the VL state may have a highlyinhomogeneous director profile, which may be relatively difficult tocompensate.

According to one embodiment of this disclosure, a negative C-platecompensator, or any compensator of similar functionality, may beinserted between the two cells as shown in FIG. 2A. Since one cell mayalways be approximately fully energized in the operation of the ZScreen,the negative C-plate can insure that the fully energized cell does notcontribute significantly to loss in FOV. Moreover, introduction of anegative C-plate between the ZScreen and the eyewear, as shown in FIG.2B, may achieve an additional FOV enhancement. The benefits of aproperly designed compensator are given by way of example.

According to the present disclosure, the Field-of-View (FOV) compensatedpolarization switch may be designed by evaluating the ON-state color andluminance uniformity, as well as the OFF-state polarization contrastratio. The OFF-state polarization contrast ratio represents the 3D ghostlevel, or cross-talk. For a system designed for maximum performance atnormal incidence, one or more of these performance metrics may bedegraded as the incidence angle is increased. The loss in performance isalso generally dependent upon the azimuth angle. The analysis discussedherein, primarily concentrates on performance at 30° incidence angle inair, which is representative of a low throw-ratio, for exampleapproximately 1.0, scenario for a cinema environment. The coloruniformity may be measured as the rms deviation in ON-state xy colorcoordinate of a particular ray through the ZScreen, relative to thenormal incidence color coordinate. This calculation is weighted by thespectrum of a typical DLP cinema projector in the full-white state.However, it does not include other second-order chromatic effects, suchas polarizer absorption and Indium Tin Oxide (ITO) absorption/reflectionwhich tend to have more impact in the blue.

TABLE 1 Performance of a ZScreen, both with and without negative C-Platecompensation at a substandard-case azimuth angle with an incidence angleof 30°. Substandard-Case State Cell 1 Cell 2 QW Compensation Output 1.ON VL VH 45 0 Δxy = 0.11 ΔL = −31.6% 2. ON VL VH 45 −550/−250 nm Δxy =0.01 ΔL = −1.1% 3. ON VH VL −45 0 Δxy = 0.13 ΔL = −31.2% 4. ON VH VL −45−550/−250 nm Δxy = 0.01 ΔL = −1.1% 5. OFF VL VH −45 0 Contrast = 2.6 6.OFF VL VH −45 −550/−250 nm Contrast = 102 7. OFF VH VL 45 0 Contrast =3.1 8. OFF VH VL 45 −550/−250 nm Contrast = 97

The ON-state spectrum of the ZScreen is associated with a zero-orderhalf-wave retarder, due to the combined action of, for example, apolycarbonate QW (eyewear) retarder with the ZScreen QW retarder. Theresults shown in Table 1 include the birefringence dispersion associatedwith both of these materials. For this particular case, the centerwavelength is selected as 516 nm. While this does not necessarilymaximize the luminance, it does provide a more balanced response betweenthe blue and red.

FIG. 3 is a graph 300 showing the spectral response for the ON-statespectrum 310 of an uncompensated ZScreen at normal incidence, as well astwo spectrums 320 and 330 with specific azimuth angles (45 azimuth and−45 azimuth) at approximately 30° off-normal. Both blue and red shiftsin the spectrum are represented, with pronounced consequences to bothbrightness and color, as viewed through the glasses at these extremeangles.

FIGS. 2A and 2B illustrate various layouts of a ZScreen with analyzingeyewear. The example layout 200 of FIG. 2A includes a first liquidcrystal cell 202, a compensator 204, a second liquid crystal cell 206and eyewear 208. The compensator Additionally, the example layout 210 ofFIG. 2B includes a first liquid crystal cell 212, a first compensator214, a second liquid crystal cell 216, a second compensator 218 andeyewear 219. The compensators of FIGS. 2A and 2B may be

A 4×4 Berreman matrix formalism may be used to trace the state ofpolarization through the structures illustrated in FIG. 2A and FIG. 2Bfor various combinations of voltage state and analyzing quarter-waveorientation. The model calculates the director profile of the π-cell ineach voltage state, and then partitions it into a sufficiently largenumber of thin homogeneous layers for matrix propagation. The LCparameters may be appropriate for a typical high-birefringence fluidused in fast-switching π-cells, with a fully energized voltage of 20V,and a holding voltage of 3.5 V. The low-voltage setting may be selectedto match the LC retardation to the analyzing quarter wave, which mayyield a high contrast at normal incidence, for example, a contrastgreater than 3,000:1.

The polarizer may have a high transmission with up to substantially 100%transmission along one direction, with substantially zero percenttransmission along the orthogonal direction. Additionally, the polarizermay contain an approximately 60 nm negative C-plate compensator oneither side of the functional layer to represent the TAC contribution.An LC cell of the Zscreen may contain a retardation range ofapproximately 500 nm to 700 nm of retardation, with some variation dueto the dispersion of LC fluid. The analyzer may be a QW retarder withapproximately 125 nm of retardation at approximately 589 nm and theapproximate dispersion of polycarbonate (PC). The negative C-platecompensator may be selected for improved FOV performance, and for thepurpose of this model, may be taken to be substantially dispersionless.

FIGS. 4 and 5 are two polar plots, 400 and 500 respectively, of theOFF-state leakage of an uncompensated ZScreen, out to a maximumincidence angle of 30°. The substandard-case azimuth performance ofazimuth angles −45 and +45 are summarized in lines 5 and 7 of Table 1,respectively. In FIG. 4, the cross hatched area 410 illustrates areas ofleakage, and the black area 420 on the plot 400, represents areas ofsubstantially no leakage. Similarly in FIG. 5, the cross hatched area510 illustrates leakage areas and the black area 520 represents areas ofsubstantially no leakage. Additionally, while the azimuth angles of −45and +45 may be different in character, the performance at thesubstandard-case azimuth angles may be similar, as shown in Table 1.Furthermore, Table 1 illustrates that an uncompensated ZScreen may haveboth a significant ON-state loss in brightness off-normal of greaterthan approximately 30%, as well as a color shift of approximately 0.13.The contrast ratio, calculated as the ratio of ON-state lumens toOFF-state lumens at approximately 30° for the substandard-case azimuthangle, is roughly 3:1. Such performance may be unacceptable for a highquality stereoscopic experience.

A first negative C-plate compensator may be inserted between the liquidcrystal cells, and a second negative C-plate compensator may be insertedbetween the ZScreen and the analyzing circular polarizer (eyewear) asshown in FIG. 2B. The system performance metrics may be evaluated as afunction of retardation value. When the retardation of the firstcompensator between the liquid crystal cells is roughly matched to thenet retardation of either one of the liquid crystal cells, and theretardation of the second compensator has roughly half of the netretardation of either one of the liquid crystal cells, improved FOVperformance may be achieved. Furthermore, the retardation of the firstnegative C-plate compensator may be in the approximate range of 60-80%of the splay state retardation of one of the first or second LC cells ofthe Zscreen.

FIG. 6A is a polar plot 600 showing an OFF-state polar leakage plot with−550 nm of negative C-plate retardation, corresponding to the stateshown in FIG. 4. FIG. 6B is a polar plot 610 showing an OFF-state polarleakage plot with −500 nm and −250 nm of negative C-plate retardation,corresponding to the state shown in FIG. 4. Plots 600 and 610 bothillustrate larger areas of little leakage or substantially no leakage ascompared to the black area 420 of FIG. 4. The areas of little leakage orsubstantially no leakage are represented as the black areas 605 and 615on respective plots 600 and 610.

FIG. 7A is a polar plot 700 showing an OFF-state polar leakage plot with−550 nm of negative C-plate retardation, corresponding to the stateshown in FIG. 5. FIG. 7B is a polar plot 710 showing an OFF-state polarleakage plot with −500 nm and −250 nm of negative C-plate retardation,also corresponding to the state shown in FIG. 5. Table 1 summarizes thesubstandard-case azimuth performance, which may improve the threeperformance metrics relative to the uncompensated case. Similar to FIGS.6A and 6B, the plots 700 and 710 of FIGS. 7A and 7B show larger areas ofsubstantially no leakage when compared to the plot 500 of FIG. 5.

Other important metrics are for ON-state performance improvement and mayshow a reduction in luminance loss and color shift. A substandard-caseluminance loss is approximately 1.1%, compared to approximately 31.6%for the uncompensated case. A substandard-case color shift isapproximately 0.01, compared to approximately 0.13 for the uncompensatedcase.

As may be used herein, the terms “substantially” and “approximately”provide an industry-accepted tolerance for its corresponding term and/orrelativity between items. Such an industry-accepted tolerance rangesfrom less than one percent to ten percent and corresponds to, but is notlimited to, component values, angles, et cetera. Such relativity betweenitems range between less than one percent to ten percent.

While various embodiments in accordance with the principles disclosedherein have been described above, it should be understood that they havebeen presented by way of example only, and not limitation. Thus, thebreadth and scope of the embodiment(s) should not be limited by any ofthe above-described exemplary embodiments, but should be defined only inaccordance with any claims and their equivalents issuing from thisdisclosure. Furthermore, the above advantages and features are providedin described embodiments, but shall not limit the application of suchissued claims to processes and structures accomplishing any or all ofthe above advantages.

Additionally, the section headings herein are provided for consistencywith the suggestions under 37 CFR 1.77 or otherwise to provideorganizational cues. These headings shall not limit or characterize theembodiment(s) set out in any claims that may issue from this disclosure.Specifically and by way of example, although the headings refer to a“Technical Field,” the claims should not be limited by the languagechosen under this heading to describe the so-called field. Further, adescription of a technology in the “Background” is not to be construedas an admission that certain technology is prior art to anyembodiment(s) in this disclosure. Neither is the “Summary” to beconsidered as a characterization of the embodiment(s) set forth inissued claims. Furthermore, any reference in this disclosure to“invention” in the singular should not be used to argue that there isonly a single point of novelty in this disclosure. Multiple embodimentsmay be set forth according to the limitations of the multiple claimsissuing from this disclosure, and such claims accordingly define theembodiment(s), and their equivalents, that are protected thereby. In allinstances, the scope of such claims shall be considered on their ownmerits in light of this disclosure, but should not be constrained by theheadings set forth herein.

1. A polarization switch that transforms linearly polarized light of aninitial polarization orientation, comprising: a first liquid crystalcell having a first axis of orientation relative to the initialpolarization orientation; a second liquid crystal cell having a secondaxis of orientation relative to the initial polarization orientation;and at least a first compensation layer located between the first liquidcrystal cell and a first side of the second liquid crystal cell, thefirst compensation layer being operable to enhance the field of viewthrough the polarization switch.
 2. The polarization switch of claim 1,wherein the first compensation layer is a negative C-plate compensator.3. The polarization switch of claim 1, wherein the first compensationlayer has a retardation that approximately matches the net retardationof the first liquid crystal cell and the second liquid crystal cell. 4.The polarization switch of claim 1, wherein the first compensation layercomprises polycarbonate.
 5. The polarization switch of claim 1, furthercomprising a second compensation layer.
 6. The polarization switch ofclaim 5, wherein the second compensation layer is adjacent to a secondside of the second liquid crystal cell.
 7. The polarization switch ofclaim 6, wherein the second compensation layer is a negative C-platecompensator.
 8. The polarization switch of claim 7, wherein the firstcompensation layer has a first compensation retardation in a range ofapproximately 60-80% of the splay-state retardation of one of the firstor second liquid crystal cells.
 9. The polarization switch of claim 8,wherein the second compensation layer has a second compensationretardation of approximately half of the splay-state retardation of oneof the first or second liquid crystal cells.
 10. A method forcompensating the angular sensitivity of a polarization switchcomprising: providing a first liquid crystal cell on an optical path;providing at least a first compensation layer located on the opticalpath after the first liquid crystal cell; and providing a second liquidcrystal cell on the optical path after the at least first compensationlayer.
 11. The method for compensating the angular sensitivity of apolarization switch of claim 10, wherein the first compensation layer isa negative C-plate compensator.
 12. The method for compensating theangular sensitivity of a polarization switch of claim 10, wherein thefirst compensation layer has a retardation that approximately matchesthe net retardation of the first liquid crystal cell and the secondliquid crystal cell.
 13. The method for compensating the angularsensitivity of a polarization switch of claim 10, wherein the firstcompensation layer has the dispersion of polycarbonate.
 14. The methodfor compensating the angular sensitivity of a polarization switch ofclaim 10, further comprising providing a second compensation layerlocated on the optical path after the second liquid crystal cell. 15.The method for compensating the angular sensitivity of a polarizationswitch of claim 10, wherein the second compensation layer is a negativeC-plate compensator.
 16. The method for compensating the angularsensitivity of a polarization switch of claim 10, wherein the firstcompensation layer has a first compensation retardation of approximately60-80% of the same splay-state retardation of one of the first or secondliquid crystal cells.
 17. The method for compensating the angularsensitivity of a polarization switch of claim 14, wherein the secondcompensation layer has a second compensation retardation ofapproximately half of the splay-state retardation of one of the first orsecond liquid crystal cells.
 18. A projection system comprising: aprojection subsystem operable to output light; and a polarizationsubsystem operable to receive the light from the projection subsystem,the polarization subsystem comprising: a first liquid crystal cell on anoptical path; at least a first compensation layer located on the opticalpath after the first liquid crystal cell; a second liquid crystal celllocated on the optical path after the at least first compensation layer;and at least a second compensation layer located on the optical pathafter the second liquid crystal cell.
 19. The projection system of claim18, wherein a substandard-case luminance loss of the projection systemis approximately 1.1%.
 20. The projection system of claim 18, wherein asubstandard-case color shift is approximately 0.01.